This is just a guess but I think they're related to the secret glitch levels that you can find by completing a level in each dark world under circumstances I don't quite understand yet.
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ManaDec 23 '10 at 19:28

Oh .. I thought they were named that way because the levels are notoriously hard, and that's what you end up with if you smash your keyboard. :)
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Steven JeurisJul 3 '11 at 22:43

The glitch Bandage girl occurs in the dark OR light world of the first 6 worlds when you die a lot. I think the number of deaths is somewhat randomized, but she makes funny bleeping sounds and is constantly morphing when she's "ready". Be sure you can get her in one shot though, because if you die again she goes back to normal and you have to die a bunch more times to maker her glitch again. As for the achievements, I'm not sure what the criteria are but it doesn't seem like you get the achievement when you beat it only, because I've beaten all of them and only have two glitch achievements.

The appearance of the glitched Bandage Girl is totally random; she could appear on the first or five hundredth attempt at a level with equal chance. I don't think the probability of her appearance is known, however.
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OedipusPrimeJan 22 '11 at 1:48

5

Discussion relative to unlocking the glitch levels can be found here. A cute picture of a kitten can be found here.
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ManaJan 22 '11 at 2:38

They're very well hidden warp zones in certain levels. I found and completed the first one, (found by completely random chance, completed in approx 1.5 hours) which unlocks the achievement. It appeared in the forest as a level coming before level 1. It is gold in colour and is known as world -1, an obvious nod to Mario. The only time I ever finished the level I luckily got an a+ on it.

They are not hidden -- they are unlocked by collecting the negative bandage girl from a dark world level.
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Raven Dreamer♦Jan 3 '11 at 5:09

They are not hidden. You must save the "glitchy" bandage girl in order to unlock the -1 glitchy level. Unfortunately, I don't know exactly how to get the bandage girl to become glitchy.
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Denilson SáJan 13 '11 at 13:21

Every time you die, there's a certain chance that Bandage Girl becomes glitchy (in that certain chapter - light or dark world doesn't matter). Save her in this glitchy state to unlock the glitch level of that chapter. Each one brings you an achievement when you beat it. As far as I know there is only A+ or death (or I somehow managed to get an A+ on everyone of the glitch levels at first try O_o). Not getting the achievement after beating the level is just a bug I think...but I'm not sure with that...